General Discussion

I imagine they'd have basically no smell, like lizards. It's been years since I last handled a lizard, but if my memory's right breathing them in felt like I was breathing in a "solid" scent even though there was no smell. So maybe that? The presence or physical feel of a smell, feeling something in the air when you breathe in but it's nothing a human can actually discern so it seems like nothing.

Anything else would probably be environmental - the smell of their lair (hopefully they relieve themselves elsewhere...), or the smell of smoke or hot air if they breathed fire recently if we go classic vs FR dragons.

I think they'd smell really earthy, like the smell of dirt after a rainstorm because they'd properly be sitting in a cave all day.
That or like an ashy firey smell.

Also depends on the dragon! I doubt a sea dragon would smell like smoke.